Class Notes

Operational Amplifiers

TODO

Sources

  1. Introduction to Operational Amplifiers (Lecture Slides)

Operational Amplifiers

  • What are operational amplifiers?
    • A direct coupled amplifier in an integrated circuit that has high gain. External feedback networks control its response.
    • It is used for mathematical operations like addition, subtraction, integration, and differentiation.
  • Operational amplifier symbols
    • - the inverting terminal
    • - the non-inverting terminal
  • Operational amplifier equivalent circuit
    • Ideal circuit
      • A - open loop gain

The Typical Operational Amplifier Block Diagram

graph LR;
IS[input stage] --> IS2[intermediate stage]
IS2 --> LS[level shifting stage]
LS --> OS[output stage]
  1. The input stage is often made up of a differential amplifier with dual inputs and a balanced output.
  2. The intermediate stage is also made up of a differential amplifier with dual-input, but has an unbalanced output
  3. The level shifting stage can be an emitter follower with either a current mirror, constant current bias, or a voltage divider.1
  4. The output stage is typically a complementary symmetry push-pull amplifier.

Operational Amplifier Parameters

  1. Input bias current
    • Is the average of the currents flowing through the two inputs.
    • Ideally the two currents have the same magnitude.
    • It is needed by the operational amplifier to work properly during the input stage.
    • Problems arise when the operational amplifier operates in high dc applications.
    • Minimizing the effects of
      • Put a dummy resistance at the positive terminal that the same magnitude as the Thevenin resistance found in the negative terminal.
      • Use a super-beta transistor at the input stage.
        • Its thin base results in high gain.
      • Use input current cancellation.
        • Dummy resistance unnecessary when this is used.
      • Use very low input bias current (like FETs and MOSFETs).
  2. Input offset current
    • Is the difference between the input bias currents ().
    • Errors also exists at high dc applications.
    • Reducing all resistances can eliminate it because it will increase power dissipation and generate harmonic distortion.
  3. Input offset voltage
    • The transistor mismatches prevents the output from becoming zero when the input is equal to zero. Nonetheless, the input offset voltage refers to the amount of voltage applied to one of the input terminals to obtain a zero output voltage.
  4. Input voltage range
    • The range of input voltages where the operational amplifier can still work properly.
      • For BJT, this is the range of input voltages where it still operates in the forward active region.
  5. Output voltage swing
    • Depends on the load resistance.
    • The limit of output voltage that the operational amplifier can push without clipping or saturation
    • CMOS operational amplifiers can give rail-to-rail outputs—their output ranges up to and down to .
  6. Output short circuit current
    • Maximum output current that the operation amplifier can supply the load
  7. Input resistance
    • The intrinsic resistance that looks into one of the inputs while the other input is grounded.
  8. Output resistance
    • The resistance that looks into the output of operational amplifiers.
  9. Supply current
    • The current the operational amplifier extracts from the power supply.
  10. Open-loop voltage gain
    • Ratio of the operational amplifier’s output voltage to input voltage with no external feedback
    • Gain and frequency has an inverse relationship (i.e. gain decreases when frequency grows)
  11. Unity gain bandwidth product
    • The frequency where the goes down to 1 or 0 dB.
  12. Common-mode rejection ratio
    • Measures the capacity of an operational amplifier to reject signals that are present at both inputs at the same time.
    • The ratio of the common-mode input voltage to the generated output voltage.
    • Can and typically expressed in dB.
  13. Slew rate
    • The output voltage’s time rate of change with a unity voltage gain.
  14. Channel separation for packages with one internal operational amplifiers
    • There will be some amount of crosstalk.2

Loop Configurations

  • Open-loop
    • for oscillator circuits and comparison
  • Closed loop
    • for amplifiers and similar uses
    • It has an external component attached between the input and output of the operational amplifier.

Types of Operational Amplifiers

  • Compensated operational amplifier
    • Internal compensation is used to minimize the instability in the amplifier.3
      • The circuit will oscillate when the total phase lag is 360 degrees
    • An RC circuit with limited high frequency gain and slew rate.
    • -20dB/decade constant roll-off rate from unity gain to fc.
  • Uncompensated operational amplifier
    • Needs an external RC circuit, and, as a result, potentially increasing frequency range of operation.
    • Frequency response depends on the individual responses of several internal stages.

Responses

  • Frequency response
    • Demonstrates the change in voltage gain as frequency also changes.
  • Phase response
    • One RC network can lead to a phase shift of up to -90 degrees.
    • Compensated operational amplifiers are more stable because the phase lag stay below 90 degrees.
    • The phase lag in an uncompensated operational amplifier is determined by the total number of stages (more stages more phase lag).
      • Total phase lag is given by the following equation:

Footnotes

  1. An emitter follower has high input impedance and low output impedance. ↩

  2. Crosstalk will occur when a signal applied to the input of the operational amplifier section results in a small output signal in the remaining section(s), despite the lack of input signal applied to unused section(s). ↩

  3. Instability is a result of feedback lag. ↩

Graph View